Here [PDF]
is a preprint of a paper I prepared from a 20 page handwritten manuscript
I found in Klarner's files entitled "Satterfield's Tomb."

Satterfield's Tomb is closely related to the geometry of 20 cannonballs
stacked in a four layer pyramid inside an enclosing and tangent regular
tetrahedron. Satterfield Tomb Animals are certain
connected unions of five Voronoi cells of the tomb, each cell
enclosing a cannonball.
Klarner and Wade Satterfield were interested in which
tomb animals could be used to pack the tomb if you're
allowed to make copies of them (or their mirror images).

The image below is a Java applet that uses the
LiveGraphics3D package.
Click and drag it to see the animal perform tricks!

The Little Bear. Four copies of this five-celled animal will
pack the tomb in three non-isomorphic ways.

Wade Satterfield sent me a photo of a model he and Klarner made of the tomb
in the 1980s.

Here's another (larger) photo of the tomb model taken from a different viewpoint
[Photo].

The images on this page are Java applets that use the
LiveGraphics3D package by Martin Kraus. By clicking and dragging your
mouse over an image, you can rotate the object. If you release a click while
dragging, you can start the object spinning
about a fixed axis. And by holding down the shift
key and dragging up or down, you can move the object closer or farther away.

Visualizing the Tomb

Satterfield's tomb is a regular tetrahedron dissected into twenty
polyhedral cells.
Each cell can be thought of as enclosing one of 20 cannonballs stacked
as a four-layer pyramid.

We usually identify animals that are identical with respect to one of the
twenty-four symmetries (rotations and reflections) of the tomb.
However we also sometimes have reason to distinguish right-
and left-handed versions of animals that themselves have no line of symmetry.

The Little Bear Packings

One Satterfield Tomb Animal is the Little Bear.

The Little Bear.

Four identical copies of the little bear will
pack Satterfield's Tomb in two non-isomorphic ways.
And if we allow ourselves to use both right- and left-handed
versions of the Little Bear, then
there are 3 non-isomorphic ways the bear will pack the tomb.

To visualize these packings, it's useful to consider the following subset S of 10 cells.

A subset S of 10 cells isomorphic to its complement S' in Satterfield's Tomb T

The subset S can be decomposed as a union of two little bears in two
different ways (stare at it!). In fact,
either two "left-handed" or two "right-handed"
bears can be used to pack both S and its (isomorphic) complement S'. Suppose
first we limit ourselves to one handedness category in packing S and S'.
Then the resulting packings of T
are always identical under one of the 24 available
reflections and/or rotations of the tomb (ie, the same isomorphism class
of packings is obtained).
But if we choose to pack S with right-handed bears,
and S' with left-handed bears (or the reverse), then a second, non-isomorphic packing is obtained.

But there is still one more way to pack the tomb with four little bears!

Another self-complement subset S'' of ten cells packable by two little bears.

If you're good at visualizing this stuff, you'll see why S'' only adds one
more isomorphism class of little bear packings to the ones described already.

Counting Satterfield Tomb Animals

The little bear is just one Satterfield Tomb animal.
Klarner and Satterfield's original
paper shows that there are nineteen
distinct Satterfield tomb animals if we treat as
identical two animals that
can be superimposed by rotating or reflecting the tomb tetrahedron.

You can find pictures of all nineteen animals in the original paper (link at the
top of the page). Here are some highlights.